Channels in a communication network may typically experience channel distortion. This channel distortion may result in intersymbol interference (ISI), which essentially is the spreading of a signal pulse outside its allocated time interval causing interference with adjacent pulses. If a communication channel is uncompensated with respect to its intersymbol interference, high error rates may result. Various methods and designs are used for compensating or reducing intersymbol interference in a signal received from a communication channel. The compensators for such intersymbol interference are known as equalizers. Various equalization methods include maximum-likelihood (ML) sequence detection, linear filters with adjustable coefficients, and decision-feedback equalization (DFE).
Linear and DFE equalizers at the receiver end of a communication system are generally accompanied with increased noise characteristics. The increased noise characteristics may be reduced with an equalizer placed at the transmitter end. Such a design relies on the channel response being a known factor to the transmitter. Since channel characteristics may vary with time, design of the complete equalizer at the transmitter end is not straight forward. However, the channel characteristics do not vary significantly over time in wire line channels. This lack of time variation allows for a DFE feedback filter to be placed at the transmitter and a DFE feedforward filter at the receiver. However, using such a DFE design may result in the signal points at the transmitter, after subtracting intersymbol interference, having a larger dynamic range than the original set of signals, thus requiring larger transmitter power. The problems associated with increased required power can be addressed with preceding information symbols prior to transmission. One precoding technique is the Tomlinson-Harahsima preceding scheme.
FIG. 1 shows a classical Tomlinson-Harashima preceding (THP) arrangement 100 for a communication channel 110. Classical Tomlinson-Harashima precoding provides for implementation of a feedback filter at the transmitter end of the communication channel with a mechanism to limit output signal amplitude. Signal samples to be transmitted in channel 110 are subjected to a feedback filter 120 defined by a polynomial B(Z) and a modulo reduction function 130, M(x), to avoid overflowing the signal bounds. Modulo reduction function 130 is a modulo operation to limit the amplitude of the signals to be transmitted into channel 110. The feedback loop is closed with feedback filter 120 coupled back to a summer 140 that receives the signal samples. At the receive end of the communication channel, a feedforward filter 150 defined by polynomial R(z) receives the transmitted symbols and provides a filtered signal to a receive modulo reduction function 160 that maps the signal to symbol estimates in an operation effectively inverse to map reduction function 130. The classical Tomlinson-Harashima precoding arrangement provides for essentially complete cancellation of intersymbol interference on systems, where the channel impulse response is stable, which is an assumption used to design the appropriate Tomlinson-Harashima precoding for the system.
FIGS. 2A-2B show a system response for an δ-impulse at a transmitter in the classical Tomlinson-Harashima of FIG. 1. FIG. 2A shows show the power vs. time relation for δ-impulse at a transmitter. The resulting system response is shown in FIG. 2B, which indicates almost complete avoidance of ISI. However, to provide higher speed reliable data communication what is needed are enhanced schemes for providing channel equalization, which at the same time can be implemented without a significant amount of complexity.